# Properties

 Label 1950.2.y.b.49.2 Level $1950$ Weight $2$ Character 1950.49 Analytic conductor $15.571$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.y (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 78) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 49.2 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.49 Dual form 1950.2.y.b.199.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.366025 - 0.633975i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.366025 - 0.633975i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.09808 + 2.36603i) q^{11} +1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.96410 + 1.13397i) q^{17} -1.00000 q^{18} +(1.09808 + 0.633975i) q^{19} -0.732051i q^{21} +(4.09808 + 2.36603i) q^{22} +(5.36603 - 3.09808i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(0.366025 + 0.633975i) q^{28} +(1.23205 + 2.13397i) q^{29} -5.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.23205 + 9.06218i) q^{37} -1.26795i q^{38} +(-0.866025 + 3.50000i) q^{39} +(9.86603 - 5.69615i) q^{41} +(-0.633975 + 0.366025i) q^{42} +(6.63397 + 3.83013i) q^{43} -4.73205i q^{44} +(-5.36603 - 3.09808i) q^{46} +8.19615 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-1.00000 - 3.46410i) q^{52} +0.464102i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.366025 - 0.633975i) q^{56} +1.26795 q^{57} +(1.23205 - 2.13397i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(-4.73205 + 2.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(-1.96410 + 1.13397i) q^{68} +(3.09808 - 5.36603i) q^{69} +(-1.09808 - 0.633975i) q^{71} +(0.500000 - 0.866025i) q^{72} -9.73205 q^{73} +(5.23205 - 9.06218i) q^{74} +(-1.09808 + 0.633975i) q^{76} +3.46410i q^{77} +(3.46410 - 1.00000i) q^{78} +9.46410 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-9.86603 - 5.69615i) q^{82} -10.1962 q^{83} +(0.633975 + 0.366025i) q^{84} -7.66025i q^{86} +(2.13397 + 1.23205i) q^{87} +(-4.09808 + 2.36603i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +6.19615i q^{92} +(-2.73205 - 4.73205i) q^{93} +(-4.09808 - 7.09808i) q^{94} +1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9 $$4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33} + 2 q^{36} + 14 q^{37} + 36 q^{41} - 6 q^{42} + 30 q^{43} - 18 q^{46} + 12 q^{47} + 6 q^{49} + 16 q^{51} - 4 q^{52} - 2 q^{56} + 12 q^{57} - 2 q^{58} + 8 q^{61} - 12 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 6 q^{68} + 2 q^{69} + 6 q^{71} + 2 q^{72} - 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} - 36 q^{82} - 20 q^{83} + 6 q^{84} + 12 q^{87} - 6 q^{88} + 12 q^{89} - 4 q^{91} - 4 q^{93} - 6 q^{94} + 12 q^{97} + 6 q^{98}+O(q^{100})$$ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^11 - 10 * q^13 + 4 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 6 * q^22 + 18 * q^23 + 14 * q^26 - 2 * q^28 - 2 * q^29 - 2 * q^32 - 6 * q^33 + 2 * q^36 + 14 * q^37 + 36 * q^41 - 6 * q^42 + 30 * q^43 - 18 * q^46 + 12 * q^47 + 6 * q^49 + 16 * q^51 - 4 * q^52 - 2 * q^56 + 12 * q^57 - 2 * q^58 + 8 * q^61 - 12 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 6 * q^68 + 2 * q^69 + 6 * q^71 + 2 * q^72 - 32 * q^73 + 14 * q^74 + 6 * q^76 + 24 * q^79 - 2 * q^81 - 36 * q^82 - 20 * q^83 + 6 * q^84 + 12 * q^87 - 6 * q^88 + 12 * q^89 - 4 * q^91 - 4 * q^93 - 6 * q^94 + 12 * q^97 + 6 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0.866025 0.500000i 0.500000 0.288675i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ −0.866025 0.500000i −0.353553 0.204124i
$$7$$ 0.366025 0.633975i 0.138345 0.239620i −0.788526 0.615002i $$-0.789155\pi$$
0.926870 + 0.375382i $$0.122489\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ 0 0
$$11$$ −4.09808 + 2.36603i −1.23562 + 0.713384i −0.968195 0.250196i $$-0.919505\pi$$
−0.267421 + 0.963580i $$0.586172\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −2.50000 + 2.59808i −0.693375 + 0.720577i
$$14$$ −0.732051 −0.195649
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.96410 + 1.13397i 0.476365 + 0.275029i 0.718900 0.695113i $$-0.244646\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 1.09808 + 0.633975i 0.251916 + 0.145444i 0.620641 0.784095i $$-0.286872\pi$$
−0.368725 + 0.929538i $$0.620206\pi$$
$$20$$ 0 0
$$21$$ 0.732051i 0.159747i
$$22$$ 4.09808 + 2.36603i 0.873713 + 0.504438i
$$23$$ 5.36603 3.09808i 1.11889 0.645994i 0.177775 0.984071i $$-0.443110\pi$$
0.941118 + 0.338078i $$0.109777\pi$$
$$24$$ 0.866025 0.500000i 0.176777 0.102062i
$$25$$ 0 0
$$26$$ 3.50000 + 0.866025i 0.686406 + 0.169842i
$$27$$ 1.00000i 0.192450i
$$28$$ 0.366025 + 0.633975i 0.0691723 + 0.119810i
$$29$$ 1.23205 + 2.13397i 0.228786 + 0.396269i 0.957449 0.288604i $$-0.0931910\pi$$
−0.728663 + 0.684873i $$0.759858\pi$$
$$30$$ 0 0
$$31$$ 5.46410i 0.981382i −0.871334 0.490691i $$-0.836744\pi$$
0.871334 0.490691i $$-0.163256\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −2.36603 + 4.09808i −0.411872 + 0.713384i
$$34$$ 2.26795i 0.388950i
$$35$$ 0 0
$$36$$ 0.500000 + 0.866025i 0.0833333 + 0.144338i
$$37$$ 5.23205 + 9.06218i 0.860144 + 1.48981i 0.871789 + 0.489881i $$0.162960\pi$$
−0.0116456 + 0.999932i $$0.503707\pi$$
$$38$$ 1.26795i 0.205689i
$$39$$ −0.866025 + 3.50000i −0.138675 + 0.560449i
$$40$$ 0 0
$$41$$ 9.86603 5.69615i 1.54081 0.889590i 0.542027 0.840361i $$-0.317657\pi$$
0.998788 0.0492283i $$-0.0156762\pi$$
$$42$$ −0.633975 + 0.366025i −0.0978244 + 0.0564789i
$$43$$ 6.63397 + 3.83013i 1.01167 + 0.584089i 0.911681 0.410899i $$-0.134785\pi$$
0.0999910 + 0.994988i $$0.468119\pi$$
$$44$$ 4.73205i 0.713384i
$$45$$ 0 0
$$46$$ −5.36603 3.09808i −0.791177 0.456786i
$$47$$ 8.19615 1.19553 0.597766 0.801671i $$-0.296055\pi$$
0.597766 + 0.801671i $$0.296055\pi$$
$$48$$ −0.866025 0.500000i −0.125000 0.0721688i
$$49$$ 3.23205 + 5.59808i 0.461722 + 0.799725i
$$50$$ 0 0
$$51$$ 2.26795 0.317576
$$52$$ −1.00000 3.46410i −0.138675 0.480384i
$$53$$ 0.464102i 0.0637493i 0.999492 + 0.0318746i $$0.0101477\pi$$
−0.999492 + 0.0318746i $$0.989852\pi$$
$$54$$ −0.866025 + 0.500000i −0.117851 + 0.0680414i
$$55$$ 0 0
$$56$$ 0.366025 0.633975i 0.0489122 0.0847184i
$$57$$ 1.26795 0.167944
$$58$$ 1.23205 2.13397i 0.161776 0.280205i
$$59$$ −6.92820 4.00000i −0.901975 0.520756i −0.0241347 0.999709i $$-0.507683\pi$$
−0.877841 + 0.478953i $$0.841016\pi$$
$$60$$ 0 0
$$61$$ −0.598076 + 1.03590i −0.0765758 + 0.132633i −0.901770 0.432215i $$-0.857732\pi$$
0.825195 + 0.564848i $$0.191065\pi$$
$$62$$ −4.73205 + 2.73205i −0.600971 + 0.346971i
$$63$$ −0.366025 0.633975i −0.0461149 0.0798733i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 4.73205 0.582475
$$67$$ 5.56218 + 9.63397i 0.679528 + 1.17698i 0.975123 + 0.221664i $$0.0711488\pi$$
−0.295595 + 0.955313i $$0.595518\pi$$
$$68$$ −1.96410 + 1.13397i −0.238182 + 0.137515i
$$69$$ 3.09808 5.36603i 0.372965 0.645994i
$$70$$ 0 0
$$71$$ −1.09808 0.633975i −0.130318 0.0752389i 0.433424 0.901190i $$-0.357305\pi$$
−0.563742 + 0.825951i $$0.690639\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −9.73205 −1.13905 −0.569525 0.821974i $$-0.692873\pi$$
−0.569525 + 0.821974i $$0.692873\pi$$
$$74$$ 5.23205 9.06218i 0.608214 1.05346i
$$75$$ 0 0
$$76$$ −1.09808 + 0.633975i −0.125958 + 0.0727219i
$$77$$ 3.46410i 0.394771i
$$78$$ 3.46410 1.00000i 0.392232 0.113228i
$$79$$ 9.46410 1.06479 0.532397 0.846495i $$-0.321291\pi$$
0.532397 + 0.846495i $$0.321291\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −9.86603 5.69615i −1.08952 0.629035i
$$83$$ −10.1962 −1.11917 −0.559587 0.828772i $$-0.689040\pi$$
−0.559587 + 0.828772i $$0.689040\pi$$
$$84$$ 0.633975 + 0.366025i 0.0691723 + 0.0399366i
$$85$$ 0 0
$$86$$ 7.66025i 0.826026i
$$87$$ 2.13397 + 1.23205i 0.228786 + 0.132090i
$$88$$ −4.09808 + 2.36603i −0.436856 + 0.252219i
$$89$$ −2.19615 + 1.26795i −0.232792 + 0.134402i −0.611859 0.790967i $$-0.709578\pi$$
0.379068 + 0.925369i $$0.376245\pi$$
$$90$$ 0 0
$$91$$ 0.732051 + 2.53590i 0.0767398 + 0.265834i
$$92$$ 6.19615i 0.645994i
$$93$$ −2.73205 4.73205i −0.283300 0.490691i
$$94$$ −4.09808 7.09808i −0.422684 0.732111i
$$95$$ 0 0
$$96$$ 1.00000i 0.102062i
$$97$$ 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i $$-0.734809\pi$$
0.977173 + 0.212445i $$0.0681426\pi$$
$$98$$ 3.23205 5.59808i 0.326486 0.565491i
$$99$$ 4.73205i 0.475589i
$$100$$ 0 0
$$101$$ −5.96410 10.3301i −0.593450 1.02789i −0.993764 0.111508i $$-0.964432\pi$$
0.400313 0.916378i $$-0.368901\pi$$
$$102$$ −1.13397 1.96410i −0.112280 0.194475i
$$103$$ 18.7321i 1.84572i 0.385131 + 0.922862i $$0.374156\pi$$
−0.385131 + 0.922862i $$0.625844\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ 0 0
$$106$$ 0.401924 0.232051i 0.0390383 0.0225388i
$$107$$ 0.169873 0.0980762i 0.0164222 0.00948139i −0.491766 0.870727i $$-0.663649\pi$$
0.508189 + 0.861246i $$0.330315\pi$$
$$108$$ 0.866025 + 0.500000i 0.0833333 + 0.0481125i
$$109$$ 5.46410i 0.523366i 0.965154 + 0.261683i $$0.0842775\pi$$
−0.965154 + 0.261683i $$0.915723\pi$$
$$110$$ 0 0
$$111$$ 9.06218 + 5.23205i 0.860144 + 0.496604i
$$112$$ −0.732051 −0.0691723
$$113$$ 16.1603 + 9.33013i 1.52023 + 0.877705i 0.999716 + 0.0238510i $$0.00759271\pi$$
0.520513 + 0.853854i $$0.325741\pi$$
$$114$$ −0.633975 1.09808i −0.0593772 0.102844i
$$115$$ 0 0
$$116$$ −2.46410 −0.228786
$$117$$ 1.00000 + 3.46410i 0.0924500 + 0.320256i
$$118$$ 8.00000i 0.736460i
$$119$$ 1.43782 0.830127i 0.131805 0.0760976i
$$120$$ 0 0
$$121$$ 5.69615 9.86603i 0.517832 0.896911i
$$122$$ 1.19615 0.108295
$$123$$ 5.69615 9.86603i 0.513605 0.889590i
$$124$$ 4.73205 + 2.73205i 0.424951 + 0.245345i
$$125$$ 0 0
$$126$$ −0.366025 + 0.633975i −0.0326081 + 0.0564789i
$$127$$ 15.4641 8.92820i 1.37222 0.792250i 0.381010 0.924571i $$-0.375576\pi$$
0.991207 + 0.132321i $$0.0422429\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 7.66025 0.674448
$$130$$ 0 0
$$131$$ 13.4641 1.17636 0.588182 0.808729i $$-0.299844\pi$$
0.588182 + 0.808729i $$0.299844\pi$$
$$132$$ −2.36603 4.09808i −0.205936 0.356692i
$$133$$ 0.803848 0.464102i 0.0697024 0.0402427i
$$134$$ 5.56218 9.63397i 0.480499 0.832249i
$$135$$ 0 0
$$136$$ 1.96410 + 1.13397i 0.168420 + 0.0972375i
$$137$$ −0.964102 + 1.66987i −0.0823688 + 0.142667i −0.904267 0.426968i $$-0.859582\pi$$
0.821898 + 0.569634i $$0.192915\pi$$
$$138$$ −6.19615 −0.527452
$$139$$ −4.92820 + 8.53590i −0.418005 + 0.724005i −0.995739 0.0922197i $$-0.970604\pi$$
0.577734 + 0.816225i $$0.303937\pi$$
$$140$$ 0 0
$$141$$ 7.09808 4.09808i 0.597766 0.345120i
$$142$$ 1.26795i 0.106404i
$$143$$ 4.09808 16.5622i 0.342698 1.38500i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 4.86603 + 8.42820i 0.402715 + 0.697523i
$$147$$ 5.59808 + 3.23205i 0.461722 + 0.266575i
$$148$$ −10.4641 −0.860144
$$149$$ 2.42820 + 1.40192i 0.198926 + 0.114850i 0.596154 0.802870i $$-0.296695\pi$$
−0.397228 + 0.917720i $$0.630028\pi$$
$$150$$ 0 0
$$151$$ 3.26795i 0.265942i −0.991120 0.132971i $$-0.957548\pi$$
0.991120 0.132971i $$-0.0424517\pi$$
$$152$$ 1.09808 + 0.633975i 0.0890657 + 0.0514221i
$$153$$ 1.96410 1.13397i 0.158788 0.0916764i
$$154$$ 3.00000 1.73205i 0.241747 0.139573i
$$155$$ 0 0
$$156$$ −2.59808 2.50000i −0.208013 0.200160i
$$157$$ 23.5885i 1.88256i 0.337622 + 0.941282i $$0.390378\pi$$
−0.337622 + 0.941282i $$0.609622\pi$$
$$158$$ −4.73205 8.19615i −0.376462 0.652051i
$$159$$ 0.232051 + 0.401924i 0.0184028 + 0.0318746i
$$160$$ 0 0
$$161$$ 4.53590i 0.357479i
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ 3.26795 5.66025i 0.255966 0.443345i −0.709192 0.705016i $$-0.750940\pi$$
0.965157 + 0.261670i $$0.0842733\pi$$
$$164$$ 11.3923i 0.889590i
$$165$$ 0 0
$$166$$ 5.09808 + 8.83013i 0.395687 + 0.685351i
$$167$$ −1.26795 2.19615i −0.0981169 0.169943i 0.812788 0.582559i $$-0.197949\pi$$
−0.910905 + 0.412616i $$0.864615\pi$$
$$168$$ 0.732051i 0.0564789i
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 0 0
$$171$$ 1.09808 0.633975i 0.0839720 0.0484812i
$$172$$ −6.63397 + 3.83013i −0.505836 + 0.292044i
$$173$$ −14.1962 8.19615i −1.07931 0.623142i −0.148602 0.988897i $$-0.547477\pi$$
−0.930711 + 0.365755i $$0.880811\pi$$
$$174$$ 2.46410i 0.186803i
$$175$$ 0 0
$$176$$ 4.09808 + 2.36603i 0.308904 + 0.178346i
$$177$$ −8.00000 −0.601317
$$178$$ 2.19615 + 1.26795i 0.164609 + 0.0950368i
$$179$$ −11.0263 19.0981i −0.824143 1.42746i −0.902573 0.430538i $$-0.858324\pi$$
0.0784298 0.996920i $$-0.475009\pi$$
$$180$$ 0 0
$$181$$ −8.80385 −0.654385 −0.327192 0.944958i $$-0.606103\pi$$
−0.327192 + 0.944958i $$0.606103\pi$$
$$182$$ 1.83013 1.90192i 0.135658 0.140980i
$$183$$ 1.19615i 0.0884221i
$$184$$ 5.36603 3.09808i 0.395589 0.228393i
$$185$$ 0 0
$$186$$ −2.73205 + 4.73205i −0.200324 + 0.346971i
$$187$$ −10.7321 −0.784805
$$188$$ −4.09808 + 7.09808i −0.298883 + 0.517680i
$$189$$ −0.633975 0.366025i −0.0461149 0.0266244i
$$190$$ 0 0
$$191$$ −3.46410 + 6.00000i −0.250654 + 0.434145i −0.963706 0.266966i $$-0.913979\pi$$
0.713052 + 0.701111i $$0.247312\pi$$
$$192$$ 0.866025 0.500000i 0.0625000 0.0360844i
$$193$$ 4.13397 + 7.16025i 0.297570 + 0.515406i 0.975579 0.219647i $$-0.0704905\pi$$
−0.678009 + 0.735053i $$0.737157\pi$$
$$194$$ −6.00000 −0.430775
$$195$$ 0 0
$$196$$ −6.46410 −0.461722
$$197$$ −4.92820 8.53590i −0.351120 0.608158i 0.635326 0.772244i $$-0.280866\pi$$
−0.986446 + 0.164086i $$0.947532\pi$$
$$198$$ 4.09808 2.36603i 0.291238 0.168146i
$$199$$ 1.90192 3.29423i 0.134824 0.233522i −0.790706 0.612196i $$-0.790286\pi$$
0.925530 + 0.378674i $$0.123620\pi$$
$$200$$ 0 0
$$201$$ 9.63397 + 5.56218i 0.679528 + 0.392326i
$$202$$ −5.96410 + 10.3301i −0.419633 + 0.726825i
$$203$$ 1.80385 0.126605
$$204$$ −1.13397 + 1.96410i −0.0793941 + 0.137515i
$$205$$ 0 0
$$206$$ 16.2224 9.36603i 1.13027 0.652562i
$$207$$ 6.19615i 0.430662i
$$208$$ 3.50000 + 0.866025i 0.242681 + 0.0600481i
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ 2.19615 + 3.80385i 0.151189 + 0.261868i 0.931665 0.363319i $$-0.118356\pi$$
−0.780476 + 0.625186i $$0.785023\pi$$
$$212$$ −0.401924 0.232051i −0.0276042 0.0159373i
$$213$$ −1.26795 −0.0868784
$$214$$ −0.169873 0.0980762i −0.0116123 0.00670435i
$$215$$ 0 0
$$216$$ 1.00000i 0.0680414i
$$217$$ −3.46410 2.00000i −0.235159 0.135769i
$$218$$ 4.73205 2.73205i 0.320495 0.185038i
$$219$$ −8.42820 + 4.86603i −0.569525 + 0.328816i
$$220$$ 0 0
$$221$$ −7.85641 + 2.26795i −0.528479 + 0.152559i
$$222$$ 10.4641i 0.702305i
$$223$$ −6.53590 11.3205i −0.437676 0.758077i 0.559834 0.828605i $$-0.310865\pi$$
−0.997510 + 0.0705277i $$0.977532\pi$$
$$224$$ 0.366025 + 0.633975i 0.0244561 + 0.0423592i
$$225$$ 0 0
$$226$$ 18.6603i 1.24126i
$$227$$ 0.901924 1.56218i 0.0598628 0.103685i −0.834541 0.550946i $$-0.814267\pi$$
0.894404 + 0.447261i $$0.147600\pi$$
$$228$$ −0.633975 + 1.09808i −0.0419860 + 0.0727219i
$$229$$ 15.8564i 1.04782i 0.851773 + 0.523910i $$0.175527\pi$$
−0.851773 + 0.523910i $$0.824473\pi$$
$$230$$ 0 0
$$231$$ 1.73205 + 3.00000i 0.113961 + 0.197386i
$$232$$ 1.23205 + 2.13397i 0.0808881 + 0.140102i
$$233$$ 19.8564i 1.30084i −0.759576 0.650418i $$-0.774594\pi$$
0.759576 0.650418i $$-0.225406\pi$$
$$234$$ 2.50000 2.59808i 0.163430 0.169842i
$$235$$ 0 0
$$236$$ 6.92820 4.00000i 0.450988 0.260378i
$$237$$ 8.19615 4.73205i 0.532397 0.307380i
$$238$$ −1.43782 0.830127i −0.0932002 0.0538091i
$$239$$ 9.66025i 0.624870i 0.949939 + 0.312435i $$0.101145\pi$$
−0.949939 + 0.312435i $$0.898855\pi$$
$$240$$ 0 0
$$241$$ −15.2321 8.79423i −0.981183 0.566486i −0.0785557 0.996910i $$-0.525031\pi$$
−0.902627 + 0.430424i $$0.858364\pi$$
$$242$$ −11.3923 −0.732325
$$243$$ −0.866025 0.500000i −0.0555556 0.0320750i
$$244$$ −0.598076 1.03590i −0.0382879 0.0663166i
$$245$$ 0 0
$$246$$ −11.3923 −0.726347
$$247$$ −4.39230 + 1.26795i −0.279476 + 0.0806777i
$$248$$ 5.46410i 0.346971i
$$249$$ −8.83013 + 5.09808i −0.559587 + 0.323077i
$$250$$ 0 0
$$251$$ 3.26795 5.66025i 0.206271 0.357272i −0.744266 0.667883i $$-0.767200\pi$$
0.950537 + 0.310611i $$0.100534\pi$$
$$252$$ 0.732051 0.0461149
$$253$$ −14.6603 + 25.3923i −0.921682 + 1.59640i
$$254$$ −15.4641 8.92820i −0.970304 0.560205i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 23.0885 13.3301i 1.44022 0.831510i 0.442355 0.896840i $$-0.354143\pi$$
0.997864 + 0.0653297i $$0.0208099\pi$$
$$258$$ −3.83013 6.63397i −0.238453 0.413013i
$$259$$ 7.66025 0.475985
$$260$$ 0 0
$$261$$ 2.46410 0.152524
$$262$$ −6.73205 11.6603i −0.415907 0.720373i
$$263$$ 24.2942 14.0263i 1.49805 0.864897i 0.498049 0.867149i $$-0.334050\pi$$
0.999997 + 0.00225153i $$0.000716686\pi$$
$$264$$ −2.36603 + 4.09808i −0.145619 + 0.252219i
$$265$$ 0 0
$$266$$ −0.803848 0.464102i −0.0492871 0.0284559i
$$267$$ −1.26795 + 2.19615i −0.0775972 + 0.134402i
$$268$$ −11.1244 −0.679528
$$269$$ −0.732051 + 1.26795i −0.0446339 + 0.0773082i −0.887479 0.460848i $$-0.847545\pi$$
0.842845 + 0.538156i $$0.180879\pi$$
$$270$$ 0 0
$$271$$ −5.07180 + 2.92820i −0.308090 + 0.177876i −0.646071 0.763277i $$-0.723589\pi$$
0.337982 + 0.941153i $$0.390256\pi$$
$$272$$ 2.26795i 0.137515i
$$273$$ 1.90192 + 1.83013i 0.115110 + 0.110764i
$$274$$ 1.92820 0.116487
$$275$$ 0 0
$$276$$ 3.09808 + 5.36603i 0.186482 + 0.322997i
$$277$$ 1.96410 + 1.13397i 0.118011 + 0.0681339i 0.557844 0.829946i $$-0.311629\pi$$
−0.439832 + 0.898080i $$0.644962\pi$$
$$278$$ 9.85641 0.591148
$$279$$ −4.73205 2.73205i −0.283300 0.163564i
$$280$$ 0 0
$$281$$ 22.3205i 1.33153i 0.746162 + 0.665765i $$0.231895\pi$$
−0.746162 + 0.665765i $$0.768105\pi$$
$$282$$ −7.09808 4.09808i −0.422684 0.244037i
$$283$$ −7.22243 + 4.16987i −0.429329 + 0.247873i −0.699061 0.715062i $$-0.746398\pi$$
0.269732 + 0.962936i $$0.413065\pi$$
$$284$$ 1.09808 0.633975i 0.0651588 0.0376195i
$$285$$ 0 0
$$286$$ −16.3923 + 4.73205i −0.969297 + 0.279812i
$$287$$ 8.33975i 0.492280i
$$288$$ 0.500000 + 0.866025i 0.0294628 + 0.0510310i
$$289$$ −5.92820 10.2679i −0.348718 0.603997i
$$290$$ 0 0
$$291$$ 6.00000i 0.351726i
$$292$$ 4.86603 8.42820i 0.284763 0.493223i
$$293$$ 7.25833 12.5718i 0.424036 0.734452i −0.572294 0.820049i $$-0.693946\pi$$
0.996330 + 0.0855965i $$0.0272796\pi$$
$$294$$ 6.46410i 0.376994i
$$295$$ 0 0
$$296$$ 5.23205 + 9.06218i 0.304107 + 0.526728i
$$297$$ 2.36603 + 4.09808i 0.137291 + 0.237795i
$$298$$ 2.80385i 0.162423i
$$299$$ −5.36603 + 21.6865i −0.310325 + 1.25416i
$$300$$ 0 0
$$301$$ 4.85641 2.80385i 0.279919 0.161611i
$$302$$ −2.83013 + 1.63397i −0.162856 + 0.0940247i
$$303$$ −10.3301 5.96410i −0.593450 0.342629i
$$304$$ 1.26795i 0.0727219i
$$305$$ 0 0
$$306$$ −1.96410 1.13397i −0.112280 0.0648250i
$$307$$ −8.58846 −0.490169 −0.245085 0.969502i $$-0.578816\pi$$
−0.245085 + 0.969502i $$0.578816\pi$$
$$308$$ −3.00000 1.73205i −0.170941 0.0986928i
$$309$$ 9.36603 + 16.2224i 0.532815 + 0.922862i
$$310$$ 0 0
$$311$$ −15.6603 −0.888012 −0.444006 0.896024i $$-0.646443\pi$$
−0.444006 + 0.896024i $$0.646443\pi$$
$$312$$ −0.866025 + 3.50000i −0.0490290 + 0.198148i
$$313$$ 13.4641i 0.761036i 0.924774 + 0.380518i $$0.124254\pi$$
−0.924774 + 0.380518i $$0.875746\pi$$
$$314$$ 20.4282 11.7942i 1.15283 0.665587i
$$315$$ 0 0
$$316$$ −4.73205 + 8.19615i −0.266199 + 0.461070i
$$317$$ 3.33975 0.187579 0.0937894 0.995592i $$-0.470102\pi$$
0.0937894 + 0.995592i $$0.470102\pi$$
$$318$$ 0.232051 0.401924i 0.0130128 0.0225388i
$$319$$ −10.0981 5.83013i −0.565384 0.326424i
$$320$$ 0 0
$$321$$ 0.0980762 0.169873i 0.00547408 0.00948139i
$$322$$ −3.92820 + 2.26795i −0.218910 + 0.126388i
$$323$$ 1.43782 + 2.49038i 0.0800026 + 0.138569i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −6.53590 −0.361990
$$327$$ 2.73205 + 4.73205i 0.151083 + 0.261683i
$$328$$ 9.86603 5.69615i 0.544760 0.314517i
$$329$$ 3.00000 5.19615i 0.165395 0.286473i
$$330$$ 0 0
$$331$$ −17.3205 10.0000i −0.952021 0.549650i −0.0583130 0.998298i $$-0.518572\pi$$
−0.893708 + 0.448649i $$0.851905\pi$$
$$332$$ 5.09808 8.83013i 0.279793 0.484616i
$$333$$ 10.4641 0.573429
$$334$$ −1.26795 + 2.19615i −0.0693791 + 0.120168i
$$335$$ 0 0
$$336$$ −0.633975 + 0.366025i −0.0345861 + 0.0199683i
$$337$$ 6.85641i 0.373492i 0.982408 + 0.186746i $$0.0597942\pi$$
−0.982408 + 0.186746i $$0.940206\pi$$
$$338$$ −11.0000 + 6.92820i −0.598321 + 0.376845i
$$339$$ 18.6603 1.01349
$$340$$ 0 0
$$341$$ 12.9282 + 22.3923i 0.700101 + 1.21261i
$$342$$ −1.09808 0.633975i −0.0593772 0.0342814i
$$343$$ 9.85641 0.532196
$$344$$ 6.63397 + 3.83013i 0.357680 + 0.206507i
$$345$$ 0 0
$$346$$ 16.3923i 0.881256i
$$347$$ 7.68653 + 4.43782i 0.412635 + 0.238235i 0.691921 0.721973i $$-0.256765\pi$$
−0.279286 + 0.960208i $$0.590098\pi$$
$$348$$ −2.13397 + 1.23205i −0.114393 + 0.0660449i
$$349$$ −16.7321 + 9.66025i −0.895646 + 0.517102i −0.875785 0.482701i $$-0.839656\pi$$
−0.0198610 + 0.999803i $$0.506322\pi$$
$$350$$ 0 0
$$351$$ 2.59808 + 2.50000i 0.138675 + 0.133440i
$$352$$ 4.73205i 0.252219i
$$353$$ 9.89230 + 17.1340i 0.526514 + 0.911949i 0.999523 + 0.0308916i $$0.00983466\pi$$
−0.473008 + 0.881058i $$0.656832\pi$$
$$354$$ 4.00000 + 6.92820i 0.212598 + 0.368230i
$$355$$ 0 0
$$356$$ 2.53590i 0.134402i
$$357$$ 0.830127 1.43782i 0.0439350 0.0760976i
$$358$$ −11.0263 + 19.0981i −0.582757 + 1.00936i
$$359$$ 23.1244i 1.22046i 0.792226 + 0.610228i $$0.208922\pi$$
−0.792226 + 0.610228i $$0.791078\pi$$
$$360$$ 0 0
$$361$$ −8.69615 15.0622i −0.457692 0.792746i
$$362$$ 4.40192 + 7.62436i 0.231360 + 0.400727i
$$363$$ 11.3923i 0.597941i
$$364$$ −2.56218 0.633975i −0.134295 0.0332293i
$$365$$ 0 0
$$366$$ 1.03590 0.598076i 0.0541473 0.0312619i
$$367$$ 12.7583 7.36603i 0.665979 0.384503i −0.128572 0.991700i $$-0.541039\pi$$
0.794551 + 0.607197i $$0.207706\pi$$
$$368$$ −5.36603 3.09808i −0.279723 0.161498i
$$369$$ 11.3923i 0.593060i
$$370$$ 0 0
$$371$$ 0.294229 + 0.169873i 0.0152756 + 0.00881937i
$$372$$ 5.46410 0.283300
$$373$$ 8.89230 + 5.13397i 0.460426 + 0.265827i 0.712223 0.701953i $$-0.247688\pi$$
−0.251797 + 0.967780i $$0.581022\pi$$
$$374$$ 5.36603 + 9.29423i 0.277471 + 0.480593i
$$375$$ 0 0
$$376$$ 8.19615 0.422684
$$377$$ −8.62436 2.13397i −0.444177 0.109905i
$$378$$ 0.732051i 0.0376526i
$$379$$ −1.26795 + 0.732051i −0.0651302 + 0.0376029i −0.532211 0.846611i $$-0.678639\pi$$
0.467081 + 0.884214i $$0.345306\pi$$
$$380$$ 0 0
$$381$$ 8.92820 15.4641i 0.457406 0.792250i
$$382$$ 6.92820 0.354478
$$383$$ 2.73205 4.73205i 0.139601 0.241797i −0.787744 0.616002i $$-0.788751\pi$$
0.927346 + 0.374206i $$0.122085\pi$$
$$384$$ −0.866025 0.500000i −0.0441942 0.0255155i
$$385$$ 0 0
$$386$$ 4.13397 7.16025i 0.210414 0.364447i
$$387$$ 6.63397 3.83013i 0.337224 0.194696i
$$388$$ 3.00000 + 5.19615i 0.152302 + 0.263795i
$$389$$ −29.7846 −1.51014 −0.755070 0.655644i $$-0.772397\pi$$
−0.755070 + 0.655644i $$0.772397\pi$$
$$390$$ 0 0
$$391$$ 14.0526 0.710668
$$392$$ 3.23205 + 5.59808i 0.163243 + 0.282746i
$$393$$ 11.6603 6.73205i 0.588182 0.339587i
$$394$$ −4.92820 + 8.53590i −0.248279 + 0.430032i
$$395$$ 0 0
$$396$$ −4.09808 2.36603i −0.205936 0.118897i
$$397$$ −0.196152 + 0.339746i −0.00984461 + 0.0170514i −0.870906 0.491450i $$-0.836467\pi$$
0.861061 + 0.508501i $$0.169800\pi$$
$$398$$ −3.80385 −0.190670
$$399$$ 0.464102 0.803848i 0.0232341 0.0402427i
$$400$$ 0 0
$$401$$ −18.9904 + 10.9641i −0.948334 + 0.547521i −0.892563 0.450922i $$-0.851095\pi$$
−0.0557713 + 0.998444i $$0.517762\pi$$
$$402$$ 11.1244i 0.554832i
$$403$$ 14.1962 + 13.6603i 0.707161 + 0.680466i
$$404$$ 11.9282 0.593450
$$405$$ 0 0
$$406$$ −0.901924 1.56218i −0.0447617 0.0775296i
$$407$$ −42.8827 24.7583i −2.12562 1.22722i
$$408$$ 2.26795 0.112280
$$409$$ 12.3564 + 7.13397i 0.610985 + 0.352752i 0.773351 0.633978i $$-0.218579\pi$$
−0.162366 + 0.986731i $$0.551912\pi$$
$$410$$ 0 0
$$411$$ 1.92820i 0.0951113i
$$412$$ −16.2224 9.36603i −0.799222 0.461431i
$$413$$ −5.07180 + 2.92820i −0.249567 + 0.144087i
$$414$$ −5.36603 + 3.09808i −0.263726 + 0.152262i
$$415$$ 0 0
$$416$$ −1.00000 3.46410i −0.0490290 0.169842i
$$417$$ 9.85641i 0.482670i
$$418$$ 3.00000 + 5.19615i 0.146735 + 0.254152i
$$419$$ −5.26795 9.12436i −0.257356 0.445754i 0.708177 0.706035i $$-0.249518\pi$$
−0.965533 + 0.260281i $$0.916185\pi$$
$$420$$ 0 0
$$421$$ 32.7128i 1.59432i 0.603765 + 0.797162i $$0.293667\pi$$
−0.603765 + 0.797162i $$0.706333\pi$$
$$422$$ 2.19615 3.80385i 0.106907 0.185168i
$$423$$ 4.09808 7.09808i 0.199255 0.345120i
$$424$$ 0.464102i 0.0225388i
$$425$$ 0 0
$$426$$ 0.633975 + 1.09808i 0.0307162 + 0.0532020i
$$427$$ 0.437822 + 0.758330i 0.0211877 + 0.0366982i
$$428$$ 0.196152i 0.00948139i
$$429$$ −4.73205 16.3923i −0.228466 0.791428i
$$430$$ 0 0
$$431$$ −9.63397 + 5.56218i −0.464052 + 0.267921i −0.713747 0.700404i $$-0.753003\pi$$
0.249694 + 0.968325i $$0.419670\pi$$
$$432$$ −0.866025 + 0.500000i −0.0416667 + 0.0240563i
$$433$$ −12.8660 7.42820i −0.618302 0.356977i 0.157906 0.987454i $$-0.449526\pi$$
−0.776208 + 0.630478i $$0.782859\pi$$
$$434$$ 4.00000i 0.192006i
$$435$$ 0 0
$$436$$ −4.73205 2.73205i −0.226624 0.130842i
$$437$$ 7.85641 0.375823
$$438$$ 8.42820 + 4.86603i 0.402715 + 0.232508i
$$439$$ 8.83013 + 15.2942i 0.421439 + 0.729954i 0.996080 0.0884515i $$-0.0281918\pi$$
−0.574642 + 0.818405i $$0.694859\pi$$
$$440$$ 0 0
$$441$$ 6.46410 0.307814
$$442$$ 5.89230 + 5.66987i 0.280268 + 0.269688i
$$443$$ 36.3923i 1.72905i 0.502589 + 0.864525i $$0.332381\pi$$
−0.502589 + 0.864525i $$0.667619\pi$$
$$444$$ −9.06218 + 5.23205i −0.430072 + 0.248302i
$$445$$ 0 0
$$446$$ −6.53590 + 11.3205i −0.309484 + 0.536042i
$$447$$ 2.80385 0.132617
$$448$$ 0.366025 0.633975i 0.0172931 0.0299525i
$$449$$ 20.1962 + 11.6603i 0.953115 + 0.550281i 0.894047 0.447973i $$-0.147854\pi$$
0.0590680 + 0.998254i $$0.481187\pi$$
$$450$$ 0 0
$$451$$ −26.9545 + 46.6865i −1.26924 + 2.19838i
$$452$$ −16.1603 + 9.33013i −0.760114 + 0.438852i
$$453$$ −1.63397 2.83013i −0.0767708 0.132971i
$$454$$ −1.80385 −0.0846588
$$455$$ 0 0
$$456$$ 1.26795 0.0593772
$$457$$ −9.33013 16.1603i −0.436445 0.755945i 0.560967 0.827838i $$-0.310429\pi$$
−0.997412 + 0.0718931i $$0.977096\pi$$
$$458$$ 13.7321 7.92820i 0.641657 0.370461i
$$459$$ 1.13397 1.96410i 0.0529294 0.0916764i
$$460$$ 0 0
$$461$$ −22.2846 12.8660i −1.03790 0.599231i −0.118661 0.992935i $$-0.537860\pi$$
−0.919237 + 0.393704i $$0.871193\pi$$
$$462$$ 1.73205 3.00000i 0.0805823 0.139573i
$$463$$ −28.0526 −1.30371 −0.651856 0.758342i $$-0.726010\pi$$
−0.651856 + 0.758342i $$0.726010\pi$$
$$464$$ 1.23205 2.13397i 0.0571965 0.0990673i
$$465$$ 0 0
$$466$$ −17.1962 + 9.92820i −0.796596 + 0.459915i
$$467$$ 12.5885i 0.582524i −0.956643 0.291262i $$-0.905925\pi$$
0.956643 0.291262i $$-0.0940752\pi$$
$$468$$ −3.50000 0.866025i −0.161788 0.0400320i
$$469$$ 8.14359 0.376036
$$470$$ 0 0
$$471$$ 11.7942 + 20.4282i 0.543449 + 0.941282i
$$472$$ −6.92820 4.00000i −0.318896 0.184115i
$$473$$ −36.2487 −1.66672
$$474$$ −8.19615 4.73205i −0.376462 0.217350i
$$475$$ 0 0
$$476$$ 1.66025i 0.0760976i
$$477$$ 0.401924 + 0.232051i 0.0184028 + 0.0106249i
$$478$$ 8.36603 4.83013i 0.382653 0.220925i
$$479$$ 22.9808 13.2679i 1.05002 0.606228i 0.127363 0.991856i $$-0.459349\pi$$
0.922654 + 0.385628i $$0.126015\pi$$
$$480$$ 0 0
$$481$$ −36.6244 9.06218i −1.66993 0.413200i
$$482$$ 17.5885i 0.801132i
$$483$$ −2.26795 3.92820i −0.103195 0.178739i
$$484$$ 5.69615 + 9.86603i 0.258916 + 0.448456i
$$485$$ 0 0
$$486$$ 1.00000i 0.0453609i
$$487$$ −10.5622 + 18.2942i −0.478618 + 0.828991i −0.999699 0.0245163i $$-0.992195\pi$$
0.521081 + 0.853507i $$0.325529\pi$$
$$488$$ −0.598076 + 1.03590i −0.0270736 + 0.0468929i
$$489$$ 6.53590i 0.295564i
$$490$$ 0 0
$$491$$ 2.63397 + 4.56218i 0.118870 + 0.205888i 0.919320 0.393511i $$-0.128740\pi$$
−0.800450 + 0.599399i $$0.795406\pi$$
$$492$$ 5.69615 + 9.86603i 0.256802 + 0.444795i
$$493$$ 5.58846i 0.251691i
$$494$$ 3.29423 + 3.16987i 0.148214 + 0.142619i
$$495$$ 0 0
$$496$$ −4.73205 + 2.73205i −0.212475 + 0.122673i
$$497$$ −0.803848 + 0.464102i −0.0360575 + 0.0208178i
$$498$$ 8.83013 + 5.09808i 0.395687 + 0.228450i
$$499$$ 32.0000i 1.43252i −0.697835 0.716258i $$-0.745853\pi$$
0.697835 0.716258i $$-0.254147\pi$$
$$500$$ 0 0
$$501$$ −2.19615 1.26795i −0.0981169 0.0566478i
$$502$$ −6.53590 −0.291711
$$503$$ 9.50962 + 5.49038i 0.424013 + 0.244804i 0.696793 0.717272i $$-0.254610\pi$$
−0.272780 + 0.962076i $$0.587943\pi$$
$$504$$ −0.366025 0.633975i −0.0163041 0.0282395i
$$505$$ 0 0
$$506$$ 29.3205 1.30346
$$507$$ −6.92820 11.0000i −0.307692 0.488527i
$$508$$ 17.8564i 0.792250i
$$509$$ −8.89230 + 5.13397i −0.394144 + 0.227559i −0.683954 0.729525i $$-0.739741\pi$$
0.289810 + 0.957084i $$0.406408\pi$$
$$510$$ 0 0
$$511$$ −3.56218 + 6.16987i −0.157581 + 0.272939i
$$512$$ 1.00000 0.0441942
$$513$$ 0.633975 1.09808i 0.0279907 0.0484812i
$$514$$ −23.0885 13.3301i −1.01839 0.587967i
$$515$$ 0 0
$$516$$ −3.83013 + 6.63397i −0.168612 + 0.292044i
$$517$$ −33.5885 + 19.3923i −1.47722 + 0.852873i
$$518$$ −3.83013 6.63397i −0.168286 0.291480i
$$519$$ −16.3923 −0.719542
$$520$$ 0 0
$$521$$ −17.4449 −0.764273 −0.382137 0.924106i $$-0.624812\pi$$
−0.382137 + 0.924106i $$0.624812\pi$$
$$522$$ −1.23205 2.13397i −0.0539254 0.0934015i
$$523$$ 31.5622 18.2224i 1.38012 0.796811i 0.387945 0.921683i $$-0.373185\pi$$
0.992173 + 0.124871i $$0.0398518\pi$$
$$524$$ −6.73205 + 11.6603i −0.294091 + 0.509381i
$$525$$ 0 0
$$526$$ −24.2942 14.0263i −1.05928 0.611575i
$$527$$ 6.19615 10.7321i 0.269909 0.467495i
$$528$$ 4.73205 0.205936
$$529$$ 7.69615 13.3301i 0.334615 0.579571i
$$530$$ 0 0
$$531$$ −6.92820 + 4.00000i −0.300658 + 0.173585i
$$532$$ 0.928203i 0.0402427i
$$533$$ −9.86603 + 39.8731i −0.427345 + 1.72709i
$$534$$ 2.53590 0.109739
$$535$$ 0 0
$$536$$ 5.56218 + 9.63397i 0.240249 + 0.416124i
$$537$$ −19.0981 11.0263i −0.824143 0.475819i
$$538$$ 1.46410 0.0631219
$$539$$ −26.4904 15.2942i −1.14102 0.658769i
$$540$$ 0 0
$$541$$ 40.3205i 1.73351i −0.498731 0.866757i $$-0.666200\pi$$
0.498731 0.866757i $$-0.333800\pi$$
$$542$$ 5.07180 + 2.92820i 0.217852 + 0.125777i
$$543$$ −7.62436 + 4.40192i −0.327192 + 0.188905i
$$544$$ −1.96410 + 1.13397i −0.0842102 + 0.0486188i
$$545$$ 0 0
$$546$$ 0.633975 2.56218i 0.0271316 0.109651i
$$547$$ 6.19615i 0.264928i −0.991188 0.132464i $$-0.957711\pi$$
0.991188 0.132464i $$-0.0422889\pi$$
$$548$$ −0.964102 1.66987i −0.0411844 0.0713334i
$$549$$ 0.598076 + 1.03590i 0.0255253 + 0.0442111i
$$550$$ 0 0
$$551$$ 3.12436i 0.133102i
$$552$$ 3.09808 5.36603i 0.131863 0.228393i
$$553$$ 3.46410 6.00000i 0.147309 0.255146i
$$554$$ 2.26795i 0.0963559i
$$555$$ 0 0
$$556$$ −4.92820 8.53590i −0.209002 0.362003i
$$557$$ −15.1865 26.3038i −0.643474 1.11453i −0.984652 0.174531i $$-0.944159\pi$$
0.341178 0.939999i $$-0.389174\pi$$
$$558$$ 5.46410i 0.231314i
$$559$$ −26.5359 + 7.66025i −1.12235 + 0.323994i
$$560$$ 0 0
$$561$$ −9.29423 + 5.36603i −0.392403 + 0.226554i
$$562$$ 19.3301 11.1603i 0.815392 0.470767i
$$563$$ 18.2487 + 10.5359i 0.769091 + 0.444035i 0.832550 0.553949i $$-0.186880\pi$$
−0.0634589 + 0.997984i $$0.520213\pi$$
$$564$$ 8.19615i 0.345120i
$$565$$ 0 0
$$566$$ 7.22243 + 4.16987i 0.303581 + 0.175273i
$$567$$ −0.732051 −0.0307432
$$568$$ −1.09808 0.633975i −0.0460743 0.0266010i
$$569$$ 19.3205 + 33.4641i 0.809958 + 1.40289i 0.912893 + 0.408200i $$0.133843\pi$$
−0.102935 + 0.994688i $$0.532823\pi$$
$$570$$ 0 0
$$571$$ 24.0526 1.00657 0.503284 0.864121i $$-0.332125\pi$$
0.503284 + 0.864121i $$0.332125\pi$$
$$572$$ 12.2942 + 11.8301i 0.514048 + 0.494642i
$$573$$ 6.92820i 0.289430i
$$574$$ −7.22243 + 4.16987i −0.301458 + 0.174047i
$$575$$ 0 0
$$576$$ 0.500000 0.866025i 0.0208333 0.0360844i
$$577$$ 0.267949 0.0111549 0.00557744 0.999984i $$-0.498225\pi$$
0.00557744 + 0.999984i $$0.498225\pi$$
$$578$$ −5.92820 + 10.2679i −0.246581 + 0.427090i
$$579$$ 7.16025 + 4.13397i 0.297570 + 0.171802i
$$580$$ 0 0
$$581$$ −3.73205 + 6.46410i −0.154832 + 0.268176i
$$582$$ −5.19615 + 3.00000i −0.215387 + 0.124354i
$$583$$ −1.09808 1.90192i −0.0454777 0.0787696i
$$584$$ −9.73205 −0.402715
$$585$$ 0 0
$$586$$ −14.5167 −0.599678
$$587$$ −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i $$-0.273781\pi$$
−0.982550 + 0.185999i $$0.940448\pi$$
$$588$$ −5.59808 + 3.23205i −0.230861 + 0.133288i
$$589$$ 3.46410 6.00000i 0.142736 0.247226i
$$590$$ 0 0
$$591$$ −8.53590 4.92820i −0.351120 0.202719i
$$592$$ 5.23205 9.06218i 0.215036 0.372453i
$$593$$ −36.8564 −1.51351 −0.756756 0.653698i $$-0.773217\pi$$
−0.756756 + 0.653698i $$0.773217\pi$$
$$594$$ 2.36603 4.09808i 0.0970792 0.168146i
$$595$$ 0 0
$$596$$ −2.42820 + 1.40192i −0.0994631 + 0.0574250i
$$597$$ 3.80385i 0.155681i
$$598$$ 21.4641 6.19615i 0.877732 0.253380i
$$599$$ 9.46410 0.386693 0.193346 0.981131i $$-0.438066\pi$$
0.193346 + 0.981131i $$0.438066\pi$$
$$600$$ 0 0
$$601$$ 2.96410 + 5.13397i 0.120908 + 0.209419i 0.920126 0.391622i $$-0.128086\pi$$
−0.799218 + 0.601041i $$0.794753\pi$$
$$602$$ −4.85641 2.80385i −0.197932 0.114276i
$$603$$ 11.1244 0.453019
$$604$$ 2.83013 + 1.63397i 0.115156 + 0.0664855i
$$605$$ 0 0
$$606$$ 11.9282i 0.484550i
$$607$$ 0.679492 + 0.392305i 0.0275797 + 0.0159232i 0.513726 0.857954i $$-0.328265\pi$$
−0.486147 + 0.873877i $$0.661598\pi$$
$$608$$ −1.09808 + 0.633975i −0.0445329 + 0.0257111i
$$609$$ 1.56218 0.901924i 0.0633026 0.0365478i
$$610$$ 0 0
$$611$$ −20.4904 + 21.2942i −0.828952 + 0.861472i
$$612$$ 2.26795i 0.0916764i
$$613$$ 5.69615 + 9.86603i 0.230065 + 0.398485i 0.957827 0.287345i $$-0.0927726\pi$$
−0.727762 + 0.685830i $$0.759439\pi$$
$$614$$ 4.29423 + 7.43782i 0.173301 + 0.300166i
$$615$$ 0 0
$$616$$ 3.46410i 0.139573i
$$617$$ −17.6244 + 30.5263i −0.709530 + 1.22894i 0.255502 + 0.966809i $$0.417759\pi$$
−0.965032 + 0.262133i $$0.915574\pi$$
$$618$$ 9.36603 16.2224i 0.376757 0.652562i
$$619$$ 10.5359i 0.423474i 0.977327 + 0.211737i $$0.0679119\pi$$
−0.977327 + 0.211737i $$0.932088\pi$$
$$620$$ 0 0
$$621$$ −3.09808 5.36603i −0.124322 0.215331i
$$622$$ 7.83013 + 13.5622i 0.313959 + 0.543794i
$$623$$ 1.85641i 0.0743754i
$$624$$ 3.46410 1.00000i 0.138675 0.0400320i
$$625$$ 0 0
$$626$$ 11.6603 6.73205i 0.466037 0.269067i
$$627$$ −5.19615 + 3.00000i −0.207514 + 0.119808i
$$628$$ −20.4282 11.7942i −0.815174 0.470641i
$$629$$ 23.7321i 0.946259i
$$630$$ 0 0
$$631$$ 41.3205 + 23.8564i 1.64494 + 0.949709i 0.979039 + 0.203671i $$0.0652874\pi$$
0.665904 + 0.746037i $$0.268046\pi$$
$$632$$ 9.46410 0.376462
$$633$$ 3.80385 + 2.19615i 0.151189 + 0.0872892i
$$634$$ −1.66987 2.89230i −0.0663191 0.114868i
$$635$$ 0 0
$$636$$ −0.464102 −0.0184028
$$637$$ −22.6244 5.59808i −0.896410 0.221804i
$$638$$ 11.6603i 0.461634i
$$639$$ −1.09808 + 0.633975i −0.0434392 + 0.0250796i
$$640$$ 0 0
$$641$$ 12.9904 22.5000i 0.513089 0.888697i −0.486796 0.873516i $$-0.661834\pi$$
0.999885 0.0151806i $$-0.00483233\pi$$
$$642$$ −0.196152 −0.00774152
$$643$$ 6.92820 12.0000i 0.273222 0.473234i −0.696463 0.717592i $$-0.745244\pi$$
0.969685 + 0.244359i $$0.0785774\pi$$
$$644$$ 3.92820 + 2.26795i 0.154793 + 0.0893697i
$$645$$ 0 0
$$646$$ 1.43782 2.49038i 0.0565704 0.0979827i
$$647$$ 22.7321 13.1244i 0.893689 0.515972i 0.0185417 0.999828i $$-0.494098\pi$$
0.875147 + 0.483856i $$0.160764\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ 37.8564 1.48599
$$650$$ 0 0
$$651$$ −4.00000 −0.156772
$$652$$ 3.26795 + 5.66025i 0.127983 + 0.221673i
$$653$$ −9.12436 + 5.26795i −0.357064 + 0.206151i −0.667792 0.744348i $$-0.732760\pi$$
0.310728 + 0.950499i $$0.399427\pi$$
$$654$$ 2.73205 4.73205i 0.106832 0.185038i
$$655$$ 0 0
$$656$$ −9.86603 5.69615i −0.385204 0.222397i
$$657$$ −4.86603 + 8.42820i −0.189842 + 0.328816i
$$658$$ −6.00000 −0.233904
$$659$$ 19.1244 33.1244i 0.744979 1.29034i −0.205225 0.978715i $$-0.565793\pi$$
0.950205 0.311627i $$-0.100874\pi$$
$$660$$ 0 0
$$661$$ 8.13397 4.69615i 0.316375 0.182659i −0.333401 0.942785i $$-0.608196\pi$$
0.649776 + 0.760126i $$0.274863\pi$$
$$662$$ 20.0000i 0.777322i
$$663$$ −5.66987 + 5.89230i −0.220200 + 0.228838i
$$664$$ −10.1962 −0.395687
$$665$$ 0 0
$$666$$ −5.23205 9.06218i −0.202738 0.351152i
$$667$$ 13.2224 + 7.63397i 0.511975 + 0.295589i
$$668$$ 2.53590 0.0981169
$$669$$ −11.3205 6.53590i −0.437676 0.252692i
$$670$$ 0 0
$$671$$ 5.66025i 0.218512i
$$672$$ 0.633975 + 0.366025i 0.0244561 + 0.0141197i
$$673$$ −12.1865 + 7.03590i −0.469756 + 0.271214i −0.716138 0.697959i $$-0.754092\pi$$
0.246381 + 0.969173i $$0.420758\pi$$
$$674$$ 5.93782 3.42820i 0.228716 0.132049i
$$675$$ 0 0
$$676$$ 11.5000 + 6.06218i 0.442308 + 0.233161i
$$677$$ 38.5359i 1.48105i 0.672026 + 0.740527i $$0.265424\pi$$
−0.672026 + 0.740527i $$0.734576\pi$$
$$678$$ −9.33013 16.1603i −0.358321 0.620631i
$$679$$ −2.19615 3.80385i −0.0842806 0.145978i
$$680$$ 0 0
$$681$$ 1.80385i 0.0691236i
$$682$$ 12.9282 22.3923i 0.495046 0.857446i
$$683$$ 18.9282 32.7846i 0.724268 1.25447i −0.235007 0.971994i $$-0.575511\pi$$
0.959275 0.282475i $$-0.0911553\pi$$
$$684$$ 1.26795i 0.0484812i
$$685$$ 0 0
$$686$$ −4.92820 8.53590i −0.188160 0.325902i
$$687$$ 7.92820 + 13.7321i 0.302480 + 0.523910i
$$688$$ 7.66025i 0.292044i
$$689$$ −1.20577 1.16025i −0.0459362 0.0442022i
$$690$$ 0 0
$$691$$ 22.8109 13.1699i 0.867767 0.501006i 0.00116153 0.999999i $$-0.499630\pi$$
0.866606 + 0.498994i $$0.166297\pi$$
$$692$$ 14.1962 8.19615i 0.539657 0.311571i
$$693$$ 3.00000 + 1.73205i 0.113961 + 0.0657952i
$$694$$ 8.87564i 0.336915i
$$695$$ 0 0
$$696$$ 2.13397 + 1.23205i 0.0808881 + 0.0467008i
$$697$$ 25.8372 0.978653
$$698$$ 16.7321 + 9.66025i 0.633317 + 0.365646i
$$699$$ −9.92820 17.1962i −0.375519 0.650418i
$$700$$ 0 0
$$701$$ −31.3205 −1.18296 −0.591480 0.806320i $$-0.701456\pi$$
−0.591480 + 0.806320i $$0.701456\pi$$
$$702$$ 0.866025 3.50000i 0.0326860 0.132099i
$$703$$ 13.2679i 0.500410i
$$704$$ −4.09808 + 2.36603i −0.154452 + 0.0891729i
$$705$$ 0 0
$$706$$ 9.89230 17.1340i 0.372302 0.644846i
$$707$$ −8.73205 −0.328403
$$708$$ 4.00000 6.92820i 0.150329 0.260378i
$$709$$ −35.3827 20.4282i −1.32882 0.767197i −0.343707 0.939077i $$-0.611683\pi$$
−0.985118 + 0.171880i $$0.945016\pi$$
$$710$$ 0 0
$$711$$ 4.73205 8.19615i 0.177466 0.307380i
$$712$$ −2.19615 + 1.26795i −0.0823043 + 0.0475184i
$$713$$ −16.9282 29.3205i −0.633966 1.09806i
$$714$$ −1.66025 −0.0621334
$$715$$ 0 0
$$716$$ 22.0526 0.824143
$$717$$ 4.83013 + 8.36603i 0.180384 + 0.312435i
$$718$$ 20.0263 11.5622i 0.747374 0.431497i
$$719$$ 11.2679 19.5167i 0.420224 0.727849i −0.575737 0.817635i $$-0.695285\pi$$
0.995961 + 0.0897860i $$0.0286183\pi$$
$$720$$ 0 0
$$721$$ 11.8756 + 6.85641i 0.442272 + 0.255346i
$$722$$ −8.69615 + 15.0622i −0.323637 + 0.560556i
$$723$$ −17.5885 −0.654122
$$724$$ 4.40192 7.62436i 0.163596 0.283357i
$$725$$ 0 0
$$726$$ −9.86603 + 5.69615i −0.366163 + 0.211404i
$$727$$ 20.9808i 0.778133i 0.921210 + 0.389067i $$0.127202\pi$$
−0.921210 + 0.389067i $$0.872798\pi$$
$$728$$ 0.732051 + 2.53590i 0.0271316 + 0.0939866i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 8.68653 + 15.0455i 0.321283 + 0.556479i
$$732$$ −1.03590 0.598076i −0.0382879 0.0221055i
$$733$$ −19.0000 −0.701781 −0.350891 0.936416i $$-0.614121\pi$$
−0.350891 + 0.936416i $$0.614121\pi$$
$$734$$ −12.7583 7.36603i −0.470919 0.271885i
$$735$$ 0 0
$$736$$ 6.19615i 0.228393i
$$737$$ −45.5885 26.3205i −1.67927 0.969528i
$$738$$ −9.86603 + 5.69615i −0.363173 + 0.209678i
$$739$$ −9.46410 + 5.46410i −0.348143 + 0.201000i −0.663867 0.747851i $$-0.731086\pi$$
0.315724 + 0.948851i $$0.397753\pi$$
$$740$$ 0 0
$$741$$ −3.16987 + 3.29423i −0.116448 + 0.121017i
$$742$$ 0.339746i 0.0124725i
$$743$$ −13.8038 23.9090i −0.506414 0.877135i −0.999972 0.00742221i $$-0.997637\pi$$
0.493558 0.869713i $$-0.335696\pi$$
$$744$$ −2.73205 4.73205i −0.100162 0.173485i
$$745$$ 0 0
$$746$$ 10.2679i 0.375936i
$$747$$ −5.09808 + 8.83013i −0.186529 + 0.323077i
$$748$$ 5.36603 9.29423i 0.196201 0.339831i
$$749$$ 0.143594i 0.00524679i
$$750$$ 0 0
$$751$$ 7.95448 + 13.7776i 0.290263 + 0.502751i 0.973872 0.227098i $$-0.0729238\pi$$
−0.683609 + 0.729849i $$0.739590\pi$$
$$752$$ −4.09808 7.09808i −0.149441 0.258840i
$$753$$ 6.53590i 0.238181i
$$754$$ 2.46410 + 8.53590i 0.0897373 + 0.310859i
$$755$$ 0 0
$$756$$ 0.633975 0.366025i 0.0230574 0.0133122i
$$757$$ −6.12436 + 3.53590i −0.222593 + 0.128514i −0.607151 0.794587i $$-0.707688\pi$$
0.384557 + 0.923101i $$0.374354\pi$$
$$758$$ 1.26795 + 0.732051i 0.0460540 + 0.0265893i
$$759$$ 29.3205i 1.06427i
$$760$$ 0 0
$$761$$ −20.1962 11.6603i −0.732110 0.422684i 0.0870836 0.996201i $$-0.472245\pi$$
−0.819194 + 0.573517i $$0.805579\pi$$
$$762$$ −17.8564 −0.646869
$$763$$ 3.46410 + 2.00000i 0.125409 + 0.0724049i
$$764$$ −3.46410 6.00000i −0.125327 0.217072i
$$765$$ 0 0
$$766$$ −5.46410 −0.197426
$$767$$ 27.7128 8.00000i 1.00065 0.288863i
$$768$$ 1.00000i 0.0360844i
$$769$$ 13.9808 8.07180i 0.504159 0.291076i −0.226270 0.974065i $$-0.572653\pi$$
0.730429 + 0.682988i $$0.239320\pi$$
$$770$$ 0 0
$$771$$ 13.3301 23.0885i 0.480073 0.831510i
$$772$$ −8.26795 −0.297570
$$773$$ −17.5359 + 30.3731i −0.630722 + 1.09244i 0.356682 + 0.934226i $$0.383908\pi$$
−0.987404 + 0.158217i $$0.949425\pi$$
$$774$$ −6.63397 3.83013i −0.238453 0.137671i
$$775$$ 0 0
$$776$$ 3.00000 5.19615i 0.107694 0.186531i
$$777$$ 6.63397 3.83013i 0.237993 0.137405i
$$778$$ 14.8923 + 25.7942i 0.533915 + 0.924768i
$$779$$ 14.4449 0.517541
$$780$$ 0 0
$$781$$ 6.00000 0.214697